There is almost nothing about a whale's body that we can relate to. They breathe air like we do. They give birth to live young like we do. But the similarities seem to stop there. Their scale, body structure, and environment are all different.

But we do have a point of connection: the eyes. Both humans and whales are mammals, so our eyes are derived from a common ancestor. Not only can we look at whales and they can look back at us, but we know enough about optics to infer their eyes' capabilities from their anatomy. Animal eyes can be imagined as technological systems evolved with biological materials.

"We will make the fairly bold claim that it is sensible to approach eyes in essentially the same way that an optical engineer might evaluate a new video camera," write Michael Land and Dan-Eric Nilsson, the authors of the Oxford University Press treatment of our topic, Animal Eyes.

Their eyes capture light in ways we can understand. Their eyes have a focal length. Their eyes have a maximum resolution.

So, what does the world look like to a whale?

Here's what got me pursuing this line of inquiry. The photographer Bryant Austin makes life-size composites of whales: humpbacks, sperm whales, minkes. The results are sublime. Each fin, each ridge in the skin, seems worth pondering. Austin is especially obsessed with photographing their eyes, and with good reason.

To create these images, Austin thought a lot about what kind of visual system could represent the experience of floating next to one of these creatures. Most whale photographers use wide-angle lenses to capture as much of the whale as possible at longer distances, but he realized that wide-angle lenses do not capture enough data to create high-resolution, life-size photographs of whales.

So, on a very fancy Hasselblad H3DII-50, Austin mounted an 80mm portrait lens with a narrow field of view. The consequences of that decision are startling: Austin has to get within ten feet of the whales, and he has to take many photographs from that distance in order to get enough photographs to stitch together the life-size portrait. In practice, that brought him eye-to-eye with these multi-ton animals time and again.

In his new book about his process, out next week, Beautiful Whale, he describes a moment where he came eye-to-eye with a sperm whale named Scar. "I lowered the camera so that our eyes could meet once again, I noticed his eye moving along the length of my body before returning to meet my gaze," Austin wrote. "As I reflect upon that moment and reconsider the question, 'What does it feel like [to be so close to whales]?' the only word that comes to mind is 'disturbing.'"

Why is it disturbing? Because, as Austin puts it, the whale challenges him "to reevaluate our perceptions of intelligent, conscious life on this planet." This mammal's eye -- lens, cornea, pupil, retina, photoreceptors and ganglion nerve cells -- is a direct passageway into its brain. And when we look at it, Austin can't help but see an intelligence there, a connection to a brain that, perhaps, works enough like ours for us to understand each other.

Coming eye-to-eye with a whale, we know what we see. We know how we see, too. Light passes into our eyes through the cornea, which actually does most of the focusing for our eyes. Then it moves through the aqueous humor, to the lens, which finishing up concentrating the light on the retina. The retina is packed with photoreceptors, the cones, which detect color, and the rods, which do not pick up color but are more sensitive in dim light. Specialized ganglion nerve cells pick up excitations from the light-sensitive cells and filter them for contrast (quite seriously: kind of like hitting the "enhance" button in Instagram). This is a wonderful operation. Leo Peichl at the Max Planck Institute for Brain Research, gave a great illustration of how important the ganglions' processing is.

"The ganglions sort of throw away the information about absolute light intensity," Peichl told me. "That's why we can read a book or newspaper at bright sunlight or candlelight, even though at bright sunlight, the black of the letters emits more light than the white paper would in candlelight." In either situation, you see black letters on white paper, even though the raw unfiltered light information is vastly different. (Though obviously, you remain aware that it is brighter outside at noon than next to a candle light.)

Our vision is best where there are the densest collections of all these specialized vision cells. In humans, that's an area called the fovea. We are a weird baseline from which to examine other eyes because we have extraordinarily sharp vision, the sharpest among mammals. Only eagles and hawks can top the discriminating performance of our eyes. We may long to see like cats at night, but our maximum visual acuity (in good light) is many times better than theirs. And bees, just as an example from outside mammalia, have the equivalent of 20/2000 vision. They see with 100 times less visual acuity than we do.

Compared with most mammals (I swear we'll get back to whales in a moment), humans have remarkable color vision as well. We can distinguish big chunks of the colors in the green, red, and blue parts of the spectrum. It's not nearly as impressive as some visual systems, which can detect other parts of the electromagnetic spectrum, but when it comes to mammals, humans and some other primates are living the technicolor dream. Color vision is trickier than it seems at first. It's not that we see blue with blue photoreceptors and red with red photoreceptors. "What provides the sensation of color is our ability to compare how much light each receptor class collects," Duke's Sonke Johnsen, author of the book Optics for Biologists, told me. The leaves of a vine reflect more green light at our eyes than the red bricks on which they are climbing. So our green photoreceptors pick up more light where the leaves are and our red photoreceptors pick up more light where the brick is.

Most mammals have dichromatic vision. They can see color, but they cannot discriminate along the red-green axis. Humans with this relatively rare type of color blindness have a hard time differentiating between red and green, as well as colors close to them like oranges and browns, as one blogger describes it, depending on how saturated and bright the color is.

In general, mammals don't have the best color vision. In part, that's because our ancestors developed trying to see in the dark, not out in the bright sunlight. "There was a time where to be a mammal was to be a small, nocturnal, rodent-like mammal," said Duke's Sonke Johnsen, author of the book, The Optics of Life. Both humans and whales retain the marks of that evolutionary path. "Our color vision is kind of a kluge," Johnsen continued. "If you look at the color vision of birds and reptiles and fish. It's very well put together, nicely optimized. You look at our trichromatic vision, it's really kind of pieced together."

Whales, unlike nocturnal rodents or ourselves, see the world in monochrome. Leo Peichl at the Max Planck Institute for Brain Research co-authored a paper with the nearly tragic title, "For whales and seals the ocean is not blue." Indeed, the first thing that we can know for sure about how whales see the world is that it exists only in shades of gray. The water we see as blue they would see as black. "They do want to see the background. They want to see animals on the background. And the animals on the background are reflecting light that's not blue," Johnsen explained. If we try to imagine what that might look like, Johnsen said perhaps we could picture a grayscale photograph of people wearing fluorescent clothes under a black light.

When it comes to the optics of whale eyes, the first difference we should note is that its cornea -- the outermost layer of the eyes -- doesn't help it nearly as much as ours helps us. We live in air, which has a different refractive index than the material of the cornea. When light enters our cornea, it bends inward. You know how pencils appear to bend when you put them in a glass of water? That's refraction, and our eyes exploit it to help focus photons on the central part of our retinas. Johnsen told me roughly 70 percent of the work of focusing light on our eyes is done by the cornea before the light even reaches the lens. But that's a clever terrestrial trick. In water, the refractive index of the cornea and water are roughly the same, which means that marine mammals don't get that pencil-going-into-water light bending help. "The lens has to do everything in the whale eye," Peichl said. While our lenses are flattish, theirs are circular in order to provide sufficient focus.

Now, when we talk about the resolution with which whales see the world, it helps to bring back the video camera metaphor for eyes. Whales, like other mammals, are trying to balance the sharpness of their eyes with their sensitivity. Sharp vision requires lots and lots of individual photoreceptors. But in low-lighting conditions, it's hard for the photoreceptors to gather enough photons. The image gets "noisy."

Photographers run into this problem all the time, too. What do you do in lower light settings? The first thing you might do is put a lens with the largest possible aperture on the camera to let in more light. The same goes for eyes: the whale's big cornea and large pupil opening means that it has a huge aperture. It's gathering up a lot of photons.

And it's got a biological mirror at the back of its eye, the tapetum lucidum, which is helping it capture even more light than our own eyes can.

But vision isn't all the optics. Other capabilities matter, too, like the size of the sensor that picks up all that light. We measure that kind of thing in the megapixels of the charge-coupled device, or CCD, in the camera. There's a similar principle at play in biological camera eyes. If an organism wants to see better, it has to have a lot of photoreceptors. More photoreceptors equals more pixels. A big difference here is that CCDs capture what hits them equally. Retinas have areas of greater or lesser rod and cone density that tends to coincide with where the light is being focused. This makes a lot of sense: Evolution has put the most sensors where the most light falls.

The light detecting system, however, is more complex than we find in any digital camera. Photoreceptors send their information to ganglion nerve cells, which integrate them, dynamically increasing the size of the photoreceptor. That increases sensitivity by cutting down on the noise problem, but it decreases the acuity because each "pixel" gets largely, i.e. it has to represent a larger portion of the physical world.

What's fascinating is that by looking at the ganglion cells, researchers can calculate the maximum resolution that a particular eye could have, inferring capabilities from the anatomy alone. That's helpful in species like whales where behavioral tests aren't generally possible.

The measurement that people tend to use here is cycles per radian, and it defines how well a given eye can discriminate between two lines next to each other. An eagle is up over 8,000 cycles per radian. A human eye registers an impressive 4175. A cat is down around 570. And researchers working with minke whales estimate that it is down with the rabbits and elephants at around 230.

Though it's probably not advisable to attempt a translation from this visual acuity to the more familiar units from your optician's office, I'm going to do it anyway. If normal human good vision is 20/20, a whale might rank somewhere like 20/240. That sounds pretty bad, but if you, like me, have a glasses prescription of -5.00, you almost certainly have worse visual acuity than a normal minke whale. (Of course, you can see colors, so count your blessings.)

But it's not easy to make the comparison between human vision and whale vision. It's definitely weirder than that. One fascinating aspect of cetacean eye anatomy is that it appears that whales don't have one central area for higher-resolution imaging like humans. Instead, they appear to have two areas of dense cell concentrations, according to a 2007 paper in the Anatomical Review. These match up with a strange feature of the cetacean pupil: It closes like a smiling mouth, and when it's very tightly constricted, it has two small circular areas that remain open.

Contrast that with the way our eyes work: when they constrict, the larger circle of our pupillary opening simply becomes a smaller circle, still focused on the on the fovea. For a whale using its eyes, two distinct spots would be in the best focus. I think that is impossible to imagine what it might be like to have two centers to one's vision.

Trying to imagine what a whale might see becomes even more difficult when we take into account the actual eye positioning for most whales. Whale eyes are located on the sides of their heads. This is roughly the opposite of our own visual system. We have two eyes facing forward with a ton of visual field overlap. Or as Herman Melville wrote in Moby Dick, "For what is it that makes the front of a man -- what, indeed, but his eyes?" His narrator is staring at a sperm whale head, a lifeless version of the same creature that Austin the photographer encountered.

Looking at the eyes, placed on opposite sides of the head, Ishmael wonders about the whale mind relative to our own:

How is it, then, with the whale? True, both his eyes, in themselves, must simultaneously act; but is his brain so much more comprehensive, combining, and subtle than man's, that he can at the same moment of time attentively examine two distinct prospects, one on one side of him, and the other in an exactly opposite direction? If he can, then is it as marvellous a thing in him, as if a man were able simultaneously to go through the demonstrations of two distinct problems in Euclid. Nor, strictly investigated, is there any incongruity in this comparison.

It is no surprise that we use the same word for refracting light into a particular location as we do for directing our consciousness to a particular idea or object: focus. We focus our attention. But what if there are multiple points of focus -- not just the two eyes, but the two focal points on the retina. To grasp after Melville's question, how could an organism make sense not just of its visual surroundings, but, its own sense of coherence or conscious unity? (I imagine the 90s sitcom, Herman's Head, in which four separate characters live within one guy's mind.)

There is just so much difference to try to cross with a human mind.

I asked Peichl and Johnsen to speculate on what it might be like to have an eye on either side of your head, dual monocular vision.

"Perhaps the two eyes get very different parts of the visual field and environment. I don't know how they integrate that," Peichl said. "Usually in the brain... there is a high connectivity that connects the two hemispheres and makes that into a perceptual unity of just one continuous visual field. Something like that probably also exists in whales because they have to have some kind of perceptive unit of their environment, a unitary percept of their environment."

And Johnsen: "They have two completely independent fields of view. God knows what they do with that. The internal perception, how do they represent that? Is it like two screens in their head? Do they stick it together? We don't deal with that because we don't have a region of our field of view that's like that," he said. "For all we know, they represent sonar information as vision. We think they hear a bunch of clicks, but for all we know, it is represented in a visual spatial form in their heads."

Then he said something that's key to understanding what we can know about the vision, and maybe the minds of whales: "All we really know is what they can't do." They don't have binocular vision. They couldn't read the big E on a chart at the eye doctor's office. Their ocean is not blue.

But when it comes to what it's like *inside* those big heads, we're almost no further along than Melville's guess more than 150 years ago.

"The whale, therefore, must see one distinct picture on this side, and another distinct picture on that side; while all between must be profound darkness and nothingness to him" he wrote. "Man may, in effect, be said to look out on the world from a sentry-box with two joined sashes for his window. But with the whale, these two sashes are separately inserted, making two distinct windows, but sadly impairing the view."

At this boundary between the brain and mind, it is tempting to both know too much and to speculate too little. I choose to believe that we can blindly cross the blankness that is the perceptual gap between intelligent species.

John Jeremiah Sullivan took up this cause in a new essay in the latest Lapham's Quarterly. He, too, reached back before the neuroscience era to come up with a way of thinking about animal consciousness. Where Descartes saw animals as automata, Baruch Spinoza saw them as more like us, and that our inability to imagine what was going on inside their brains was not proof that the lights were on, but that nobody was home.

"Accepting that no two consciousnesses can ever have transparency, or at any rate can never have certainty about it, leaves us on some level cosmically alone," Sullivan writes. "Spinoza takes the notion in stride. He'd be more prone to say, Well, no doubt we sometimes understand each other."

Coming improbably eye-to-eye in the ocean, in a monochrome or trichome moment of wonder, a human and a whale could even be sharing a thought,: "Hello, intelligent creature floating in the sea. Don't kill me."

In Beautiful Whale, Austin describes an encounter with Ella, a curious minke whale off the coast of Australia. He was taking photographs as Ella swam around. The whale liked to look at him head on, a fact that Austin used to maneuver her into better lighting. Her desire to see his face was strong enough that she'd swim around him, if he turned his back to her.

"This requires some discipline and trust in the whales. At times Ella would initiate a close inspection of me from behind, where ambient lighting was poor. Peering over my shoulder, I could see her body pass by less than six feet away. I turned back to face forward, trusting her not to accidentally harm me," Austin writes. "In my experience working with whales this way, our eyes seem to gravitate toward each other."

On that particular day, he spent six hours with the whale. At one point, he hopped out of the water to change batteries and memory cards. As he was standing on the deck, one of the animals went vertical and popped its head out of the water, which is called "spyhopping."

The animal looked directly at Austin, and looking back, he saw a distinctive marking: it was Ella. She was keeping an eye on him.